Stochastic Calculus: Applications in Science and Engineering

By Mircea Dan Grigoriu. 2002

401 citations recorded by the source corpus.

Subfields: Finance, Mathematical Physics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/c6f7e2d4dd14d21de6f2928d7ca8d1afce9b57dc

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Citations in the corpus

Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion (2012, methodology): “One-dimensional aPC We will consider a stochastic process in the probability space ðO,A,GÞ with space of events O, s-algebra A and probability measure G, see e.g. [22].”
Continuous wind speed models based on stochastic differential equations (2013, background): “Therefore, a standard Wiener process describes a continuous Gaussian process whose sample paths (increments) are of unbounded variation [36].”
Relativistic Brownian Motion (2008, methodology): “B˙ are suﬃciently smooth functions so that this integral exists in the sense of Riemann-Stieltjes; in this case, the value of the integral (A.3) is independent of the underlying discretization scheme [76]. 105 A.1 Ito integral We ﬁrst summarize the properties of Ito’s stochastic integral [60, 61]. I”
A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2007, methodology): “, [33] for a technique to express a stationary random field with given covariance structure and marginal distribution D ow nl oa de d 05 /2 1/ 15 to 1 09 .”
A generalized dimension‐reduction method for multidimensional integration in stochastic mechanics (2004, methodology): “Analytical methods, which include Taylor expansion or perturbation methods [7–10], the Neumann expansion method [11–15], the decomposition method [16, 17], the polynomial chaos expansion method [14], the statistically equivalent solution [18], the point estimate method [19] and others [1], are tradi”
A univariate dimension-reduction method for multi-dimensional integration in stochastic mechanics (2004, methodology): “However, depending on the order of polynomial expansion, this method may provide inaccurate estimates of higher-order moments (e.g. skewness, kurtosis, etc.), as recently demonstrated by Grigoriu [1].”
Global sensitivity analysis: a flexible and efficient framework with an example from stochastic hydrogeology (2012, background): “[41]) and if P̂ j (ω j) is an orthonormal basis, then by definition of orthogonality: ∫”
Recent Developments in Spectral Stochastic Methods for the Numerical Solution of Stochastic Partial Differential Equations (2009, background): “For an introduction to random processes, the reader can refer to [37,67,1,77,78] for a mathematical point of view or to [98,52,53,126,30] for more technical aspects.”
Interacting Particle Solutions of Fokker–Planck Equations Through Gradient–Log–Density Estimation (2020, background): “Conversely, semi-analytical approaches try to reduce the number of required computations by assuming conditional Gaussian structures [8], or by employing cumulant neglect closures [9], statistical linearisation [10,11], or stochastic averaging [12].”