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Manipulating Stochastic Differential Equations and Stochastic Integrals
2015Many of the calculations of derivative security pricing involve formal manipulations of stochastic differential equations and stochastic integrals. This chapter derives those that are most frequently used. We also consider transformation of correlated Wiener processes to uncorrelated Wiener processes for higher dimensional stochastic differential ...
Carl Chiarella +2 more
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Equations for stochastic path integrals
Mathematical Proceedings of the Cambridge Philosophical Society, 1961Apart from the study of the integralwhere {X(u)} is a stationary Gaussian process with autocorrelation function ρ(t), by Kac and Siegert(1), most stochastic functionals of the general typehave been considered for {X(u)} either additive or Markovian (see, for example, (2), (3)), and in the Markovian case only for diffusion-type processes (Darling and ...
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Langevin equations and stochastic integrals
Zeitschrift f�r Physik B Condensed Matter and Quanta, 1978The ambiguity of stochastic integrals involved in Langevin equations is removed by the postulate of invariance with respect to nonlinear transformations of the coordinates. The Stratonovich sense of the integrals, which is imposed thereby, is also strongly suggested by stability considerations requiring small changes of the solutions whenever the ...
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Stochastic Integrals and Differential Equations
2004This chapter provides the tools needed for option pricing. The field of stochastic processes in continuous time, which are defined as solutions of stochastic differential equations, has an important role to play. To illustrate these notions we use repeated approximations by stochastic processes in discrete time and refer to the results from Chapter 4.
Jürgen Franke +2 more
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Connections between Stochastic and Ordinary Integral Equations
Advances in Applied Probability, 1980Let σ: ℝn → M m,n (the space of matrices with m columns and n rows) and b: ℝn → ℝn be two Lipschitz continuousmaps. Suppose that σ is of class C2. Let B = (Bt)t≥0 (B0 = 0) be a standard ℝm valued Brownian motion defined on a probability space (Ω,ƒ, ƒt, P). Consider the solution Xx of the following equation: $$ X_{t}^{X} = x + s.\int_{0}^{t} {\sigma (
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An overview of real‐world data sources for oncology and considerations for research
Ca-A Cancer Journal for Clinicians, 2022Lynne Penberthy +2 more
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The mechanisms of integral membrane protein biogenesis
Nature Reviews Molecular Cell Biology, 2021Ramanujan Shankar Hegde, Robert J Keenan
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Antibiofilm activity of host defence peptides: complexity provides opportunities
Nature Reviews Microbiology, 2021, Morgan A Alford, Evan F Haney
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Stochastic Integrals and Stochastic Functional Equations
SIAM Journal on Applied Mathematics, 1969openaire +1 more source