Topic

# Continuous-time stochastic process

About: Continuous-time stochastic process is a research topic. Over the lifetime, 5544 publications have been published within this topic receiving 216211 citations. The topic is also known as: continuous-space-time stochastic process.

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TL;DR: In this article, a method for making successive experiments at levels x1, x2, ··· in such a way that xn will tend to θ in probability is presented.

Abstract: Let M(x) denote the expected value at level x of the response to a certain experiment. M(x) is assumed to be a monotone function of x but is unknown to the experimenter, and it is desired to find the solution x = θ of the equation M(x) = α, where a is a given constant. We give a method for making successive experiments at levels x1, x2, ··· in such a way that xn will tend to θ in probability.

9,312 citations

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01 Jun 1992

TL;DR: In this article, a time-discrete approximation of deterministic Differential Equations is proposed for the stochastic calculus, based on Strong Taylor Expansions and Strong Taylor Approximations.

Abstract: 1 Probability and Statistics- 2 Probability and Stochastic Processes- 3 Ito Stochastic Calculus- 4 Stochastic Differential Equations- 5 Stochastic Taylor Expansions- 6 Modelling with Stochastic Differential Equations- 7 Applications of Stochastic Differential Equations- 8 Time Discrete Approximation of Deterministic Differential Equations- 9 Introduction to Stochastic Time Discrete Approximation- 10 Strong Taylor Approximations- 11 Explicit Strong Approximations- 12 Implicit Strong Approximations- 13 Selected Applications of Strong Approximations- 14 Weak Taylor Approximations- 15 Explicit and Implicit Weak Approximations- 16 Variance Reduction Methods- 17 Selected Applications of Weak Approximations- Solutions of Exercises- Bibliographical Notes

6,284 citations

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20 Dec 1990TL;DR: In this article, a representation of stochastic processes and response statistics are represented by finite element method and response representation, respectively, and numerical examples are provided for each of them.

Abstract: Representation of stochastic processes stochastic finite element method - response representation stochastic finite element method - response statistics numerical examples.

5,495 citations

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01 Jan 1990

TL;DR: In this article, the authors propose a method for general stochastic integration and local times, which they call Stochastic Differential Equations (SDEs), and expand the expansion of Filtrations.

Abstract: I Preliminaries.- II Semimartingales and Stochastic Integrals.- III Semimartingales and Decomposable Processes.- IV General Stochastic Integration and Local Times.- V Stochastic Differential Equations.- VI Expansion of Filtrations.- References.

5,254 citations

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01 Jan 1979

TL;DR: An electromagnetic pulse counter having successively operable, contact-operating armatures that are movable to a rest position, an intermediate position and an active position between the main pole and the secondary pole of a magnetic circuit.

Abstract: An electromagnetic pulse counter having successively operable, contact-operating armatures. The armatures are movable to a rest position, an intermediate position and an active position between the main pole and the secondary pole of a magnetic circuit.

4,897 citations