Heat equation with a general stochastic measure on nested fractals

Statistics & Probability Letters ◽

10.1016/j.spl.2011.12.013 ◽

2012 ◽

Vol 82 (3) ◽

pp. 699-704 ◽

Author(s):

Vadym Radchenko ◽

Martina Zähle

Keyword(s):

Heat Equation ◽

Stochastic Measure ◽

General Stochastic

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Mild solution of the heat equation with a general stochastic measure

Studia Mathematica ◽

10.4064/sm194-3-2 ◽

2009 ◽

Vol 194 (3) ◽

pp. 231-251 ◽

Author(s):

Vadym Radchenko

Keyword(s):

Heat Equation ◽

Mild Solution ◽

Stochastic Measure ◽

General Stochastic

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Properties of integrals with respect to a general stochastic measure in a stochastic heat equation

Theory of Probability and Mathematical Statistics ◽

10.1090/s0094-9000-2011-00830-7 ◽

2011 ◽

Vol 82 ◽

pp. 103-114 ◽

Author(s):

V. M. Radchenko

Keyword(s):

Heat Equation ◽

Stochastic Heat Equation ◽

Stochastic Measure ◽

General Stochastic

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Heat equation in a multidimensional domain with a general stochastic measure

Theory of Probability and Mathematical Statistics ◽

10.1090/tpms/991 ◽

2017 ◽

Vol 93 ◽

pp. 1-17 ◽

Author(s):

I. M. Bodnarchuk ◽

G. M. Shevchenko

Keyword(s):

Heat Equation ◽

Stochastic Measure ◽

Multidimensional Domain ◽

General Stochastic

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Heat equation with general stochastic measure colored in time

Modern Stochastics Theory and Applications ◽

10.15559/14-vmsta14 ◽

2014 ◽

Vol 1 (2) ◽

pp. 129-138 ◽

Author(s):

Vadym Radchenko

Keyword(s):

Heat Equation ◽

Stochastic Measure ◽

General Stochastic

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Averaging principle for the heat equation driven by a general stochastic measure

Statistics & Probability Letters ◽

10.1016/j.spl.2018.11.024 ◽

2019 ◽

Vol 146 ◽

pp. 224-230 ◽

Author(s):

Vadym Radchenko

Keyword(s):

Heat Equation ◽

Averaging Principle ◽

Stochastic Measure ◽

General Stochastic

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Strong Convergence Rate in Averaging Principle for the Heat Equation Driven by a General Stochastic Measure

Communications on Stochastic Analysis ◽

10.31390/cosa.13.2.01 ◽

2019 ◽

Vol 13 (2) ◽

Author(s):

Vadym Radchenko

Keyword(s):

Convergence Rate ◽

Heat Equation ◽

Strong Convergence ◽

Averaging Principle ◽

Stochastic Measure ◽

Strong Convergence Rate ◽

General Stochastic

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Wave equation in the plane driven by a general stochastic measure

Theory of Probability and Mathematical Statistics ◽

10.1090/tpms/1063 ◽

2019 ◽

Vol 98 ◽

pp. 73-90 ◽

Author(s):

I. M. Bodnarchuk ◽

V. M. Radchenko

Keyword(s):

Wave Equation ◽

Stochastic Measure ◽

General Stochastic

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Existence of Solution of the Dirichlet Problem for the Heat-Conduction Equation with General Stochastic Measure

Journal of Mathematical Sciences ◽

10.1007/s10958-019-04351-5 ◽

2019 ◽

Vol 240 (3) ◽

pp. 249-255

Author(s):

M. F. Horodnii

Keyword(s):

Heat Conduction ◽

Dirichlet Problem ◽

Heat Conduction Equation ◽

Existence Of Solution ◽

Conduction Equation ◽

Stochastic Measure ◽

General Stochastic

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Existence of the Solution of Neumann Problem for the Heat-Conduction Equation with General Stochastic Measure

Journal of Mathematical Sciences ◽

10.1007/s10958-016-2982-z ◽

2016 ◽

Vol 217 (4) ◽

pp. 418-426

Author(s):

M. F. Horodnii ◽

D. M. Polyulya

Keyword(s):

Heat Conduction ◽

Neumann Problem ◽

Heat Conduction Equation ◽

Conduction Equation ◽

Stochastic Measure ◽

General Stochastic

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RANDOM FIELDS: NON-ANTICIPATING DERIVATIVE AND DIFFERENTIATION FORMULAS

Infinite Dimensional Analysis Quantum Probability and Related Topics ◽

10.1142/s0219025707002828 ◽

2007 ◽

Vol 10 (03) ◽

pp. 465-481 ◽

Author(s):

GIULIA DI NUNNO

Keyword(s):

Random Fields ◽

Random Variables ◽

Explicit Formulas ◽

Stochastic Measure ◽

Stochastic Derivative ◽

Differentiation Formulas ◽

General Stochastic

The non-anticipating stochastic derivative represents the integrand in the best L2-approximation for random variables by Itô non-anticipating integrals with respect to a general stochastic measure with independent values on a space–time product. In this paper some explicit formulas for this derivative are obtained.

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