Showing papers in "Stochastic Processes and their Applications in 2019"

TL;DR: In this article, an upper bound on the error of the first-order Langevin Monte Carlo (LMC) algorithm with optimized varying step-size was established. But the error was not shown to be horizon free.

TL;DR: In this article, the existence and uniqueness of distribution dependent SDEs with non-degenerate noise were proved under integrability conditions on distribution dependent coefficients, and the coefficients were Dini continuous in the space variable.

TL;DR: In this paper, the Tamed Unadjusted Langevin Algorithm (TULA) was introduced to obtain nonasymptotic bounds in V-total variation norm and Wasserstein distance between the iterates of TULA and π.

TL;DR: In this paper, a method based on Bernstein functions was proposed to unify three different approaches in the literature, including power law relaxation, semi-Markov process and semi-Maximax relaxation.

TL;DR: In this paper, the authors proposed and analyzed explicit and easily implementable temporal numerical approximation schemes for additive noise-driven stochastic partial differential equations (SPDEs) with polynomial nonlinearities.

TL;DR: In this article, the convergence rate of partial sums of polynomial functionals of general stationary and asymptotically stationary Gaussian sequences was studied using tools from analysis on Wiener space.

TL;DR: In this paper, the existence and continuity of the transition probability density of the corresponding Markov process and a representation of this density with an explicitly given principal part and residual part are given.

TL;DR: In this article, a stochastic optimal control problem for a partially observed diffusion is studied and a corresponding randomized dynamic programming principle for the value function is obtained from a flow property of an associated filter process.

TL;DR: In this paper, the convergence of finite state symmetric N -player differential games, where players control their transition rates from state to state, to a limiting dynamics given by a finite state Mean Field Game system made of two coupled forward-backward ODEs is studied.

TL;DR: In this article, weakly interacting diffusions on time varying random graphs are considered and a central limit theorem is established for the single-type population case under stronger conditions on the edge probability function.

TL;DR: In this paper, the authors give local and global existence and uniqueness results for multidimensional coupled FBSDEs for generators with arbitrary growth in the control variable, based on Malliavin calculus arguments for Markovian equations.

TL;DR: In this article, a bound on the distance between finitely supported elements and general elements of the unit sphere of l 2 (N ∗ ) is provided. But the main application is towards the computation of quantitative rates of convergence for non-central asymptotic of sequences of quadratic forms.

TL;DR: In this paper, a Vasicek-type model for Hermite processes of order q ≥ 1 and self-similarity parameter H ∈ ( 1 2, 1 ) is presented.

TL;DR: In this article, the authors established the exponential convergence with respect to the L 1 -Wasserstein distance and the total variation for the semigroup corresponding to the stochastic differential equation d X t = d Z t + b ( X t ) d t, where ( Z t ) t ≥ 0 is a pure jump Levy process whose Levy measure ν fulfills inf x ∈ R d, | x | ≤ κ 0 [ ν ∧ ( δ x ∗ ν ) ] ( R d ) > 0 for some constant κ ≥

TL;DR: In this article, an explicit solution triplet (Y, Z, K ) to the backward stochastic Volterra integral equation (BSVIE) of linear type was presented, driven by a Brownian motion and a compensated Poisson random measure.

TL;DR: In this paper, Fernholz and Karatzas introduced polynomial processes in the context of stochastic portfolio theory to model simultaneously companies' market capitalizations and corresponding market weights.

TL;DR: In this paper, a representation of adapted M-solutions is established by means of the so-called representation partial differential equations and (forward) stochastic differential equations, and the well-posedness of the representation is also proved in certain sense.

TL;DR: In this article, a continuous-state polynomial branching process is constructed as the pathwise unique solution of a stochastic integral equation with absorbing boundary condition, which can also be obtained from a spectrally positive Levy process through Lamperti type transformations.

TL;DR: In this article, a certain class of fractional processes can be represented as linear functionals of an infinite dimensional affine process, which can be derived from integral representations similar to those of Carmona, Coutin, Montseny, and Muravlev.

TL;DR: In this article, the authors studied the nonlinear stochastic partial differential equation of fractional orders both in space and time variables, and derived the existence and uniqueness of solution together with the moment bounds of the solution under Dalang's condition.

TL;DR: In this article, the authors investigated the percolation probability of Cox point processes driven by random intensity measures and derived sufficient conditions for the existence of non-trivial sub-and super-critical percolations.

TL;DR: In this paper, the authors consider a stationary regularly varying time series which can be expressed as a function of a geometrically ergodic Markov chain and obtain practical conditions for the weak convergence of the tail array sums and feasible estimators of cluster statistics.

TL;DR: In this paper, the authors show that the Euler-Maruyama approximation converges strongly to a solution of the SDE with an explicitly given rate, depending on the regularity of b and the behaviour of the Levy measure at the origin.

TL;DR: In this paper, the authors obtained estimation error rates for estimators obtained by aggregation of reg-ularized median-of-means tests, following a construction of Le Cam.

TL;DR: In this paper, the authors used SDEs to derive corresponding limit laws for starting points of the form k ⋅ x for k → ∞ with x in the interior of the corresponding Weyl chambers.

TL;DR: In this article, the authors study the optimal sustainable harvesting of a population that lives in a random environment and prove that there exists a unique optimal harvesting strategy characterized by an optimal threshold below which the population is maintained at all times by utilizing a local time push-type policy.

TL;DR: In this paper, the authors consider a system of forward-backward stochastic differential equations (FBSDEs) with monotone functionals and show that such a system is well-posed by the method of continuation similarly to Peng and Wu (1999) for classical FBSDE.

TL;DR: In this article, under the assumption that the driving Levy process is locally stable, the authors extend the Gaussian framework into a non-Gaussian counterpart, by introducing a novel quasi-likelihood function formally based on the small-time stable approximation of the unknown transition density.

TL;DR: In this article, the authors consider reflected backward stochastic different equations with optional barrier and so-called regulated trajectories, i.e. trajectories with left and right finite limits.

TL;DR: In this article, the authors show that the specific case of conditioning to avoid the origin corresponds to a classical Cramer-Esscher-type transform to the Markov Additive Process (MAP) that underlies the Lamperti-Kiu representation of a real self-similar Markov process.