Displaying similar documents to “Stochastic Solution of a KPP-Type Nonlinear Fractional Differential Equation”

Equations in differentials in the algebra of generalized stochastic processes

Nadzeya V. Bedziuk, Aleh L. Yablonski (2010)

Banach Center Publications

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We consider an ordinary or stochastic nonlinear equation with generalized coefficients as an equation in differentials in the algebra of new generalized functions in the sense of [8]. Consequently, the solution of such an equation is a new generalized function. We formulate conditions under which the solution of a given equation in the algebra of new generalized functions is associated with an ordinary function or process. Moreover the class of all possible associated functions and processes...

Tightness of Continuous Stochastic Processes

Michał Kisielewicz (2006)

Discussiones Mathematicae Probability and Statistics

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Some sufficient conditins for tightness of continuous stochastic processes is given. It is verified that in the classical tightness sufficient conditions for continuous stochastic processes it is possible to take a continuous nondecreasing stochastic process instead of a deterministic function one.

A second order SDE for the Langevin process reflected at a completely inelastic boundary

Jean Bertoin (2008)

Journal of the European Mathematical Society

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It was shown in [2] that a Langevin process can be reflected at an energy absorbing boundary. Here, we establish that the law of this reflecting process can be characterized as the unique weak solution to a certain second order stochastic differential equation with constraints, which is in sharp contrast with a deterministic analog.

Splitting the conservation process into creation and annihilation parts

Nicolas Privault (1998)

Banach Center Publications

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The aim of this paper is the study of a non-commutative decomposition of the conservation process in quantum stochastic calculus. The probabilistic interpretation of this decomposition uses time changes, in contrast to the spatial shifts used in the interpretation of the creation and annihilation operators on Fock space.

Fractional Fokker-Planck-Kolmogorov type Equations and their Associated Stochastic Differential Equations

Hahn, Marjorie, Umarov, Sabir (2011)

Fractional Calculus and Applied Analysis

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MSC 2010: 26A33, 35R11, 35R60, 35Q84, 60H10 Dedicated to 80-th anniversary of Professor Rudolf Gorenflo There is a well-known relationship between the Itô stochastic differential equations (SDEs) and the associated partial differential equations called Fokker-Planck equations, also called Kolmogorov equations. The Brownian motion plays the role of the basic driving process for SDEs. This paper provides fractional generalizations of the triple relationship between the driving...