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Teoriya Veroyatnostei i ee Primeneniya, 2013, Volume 58, Issue 2, Pages 255–281
DOI: https://doi.org/10.4213/tvp4506 (Mi tvp4506) 		 
This article is cited in 4 scientific papers (total in 4 papers)

On a probabilistic method of solving a one-dimensional initial-boundary value problem

I. A. Ibragimova, N. V. Smorodinab, M. M. Faddeevb

a St. Petersburg Department of V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences
b St. Petersburg State University, Department of Mathematics and Mechanics
Full-text PDF (272 kB) Citations (4)
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DOI: https://doi.org/10.4213/tvp4506
Abstract: We obtain an analogue of probabilistic representation of a solution of an initial-boundary value problem for the equation ∂u/∂t+(σ2/2)∂2u/∂x2+f(x)u=0, where σ is a complex number.
Keywords: random processes; evolution equation; limit theorems; Feynman–Kac formula; Feynman integral; Feynman measure.
Received: 01.11.2012
English version:
Theory of Probability and its Applications, 2014, Volume 58, Issue 2, Pages 242–263
DOI: https://doi.org/10.1137/S0040585X97986503
Bibliographic databases:
Document Type: Article
MSC: 60
Language: Russian
Citation: I. A. Ibragimov, N. V. Smorodina, M. M. Faddeev, “On a probabilistic method of solving a one-dimensional initial-boundary value problem”, Teor. Veroyatnost. i Primenen., 58:2 (2013), 255–281; Theory Probab. Appl., 58:2 (2014), 242–263
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  • https://www.mathnet.ru/eng/tvp4506
  • https://doi.org/10.4213/tvp4506
  • https://www.mathnet.ru/eng/tvp/v58/i2/p255
    • This publication is cited in the following 4 articles:
    1. Faddeev M.M., Ibragimov I.A., Smorodina N.V., “A Stochastic Interpretation of the Cauchy Problem Solution For the Equation Partial Derivative ∂tu=(σ2/2)Δu+V(x)u with complex σ”, Markov Process. Relat. Fields, 22:2 (2016), 203–226  mathscinet  zmath  isi
    2. I. A. Ibragimov, N. V. Smorodina, M. M. Faddeev, “Limit theorems for symmetric random walks and probabilistic approximation of the Cauchy problem solution for Schrödinger type evolution equations”, Stochastic Process. Appl., 125:12 (2015), 4455–4472  crossref  mathscinet  zmath  isi  elib
    3. A. Lachal, “First exit time from a bounded interval for pseudo-processes driven by the equation ∂/∂t=(−1)N−1∂2N/∂x2N”, Stochastic Process. Appl., 124:2 (2014), 1084–1111  crossref  mathscinet  zmath  isi
    4. I. A. Ibragimov, N. V. Smorodina, M. M. Faddeev, “Limit theorems on convergence of expectations of functionals of sums of independent random variables to solutions of initial boundary value problems”, Theory Probab. Appl., 59:2 (2015), 244–259  mathnet  crossref  crossref  isi  elib  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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