Robert C. Dalang's Books

Seminar on Stochastic Analysis, Random Fields and Application [sic].

Centro Stefano Fransicni [sic], Ascona, September 1999. III

By: Robert C. Dalang,Marco Dozzi,Francesco Russo

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Seminar on Stochastic Analysis, Random Fields and Application [sic].

Centro Stefano Fransicni [sic], Ascona, September 1999. III

By: Robert C. Dalang,Marco Dozzi,Francesco Russo

This volume contains 20 refereed research or review papers presented at the five-day Third Seminar on Stochastic Analysis, Random Fields and Applications which took place at the Centro Stefano Franscini (Monte Verità) in Ascona, Switzerland, from September 20 to 24, 1999. The seminar focused on three topics: fundamental aspects of stochastic analysis, physical modeling, and applications to financial engineering. The third topic was the subject of a mini-symposium on stochastic methods in financial models.

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Page Count

328

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3764367210

ISBN 13

9783764367213

Hitting Probabilities for Nonlinear Systems of Stochastic Waves

By: Robert C. Dalang,Marta Sanz-Solé

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Hitting Probabilities for Nonlinear Systems of Stochastic Waves

By: Robert C. Dalang,Marta Sanz-Solé

The authors consider a d-dimensional random field u={u(t,x)} that solves a non-linear system of stochastic wave equations in spatial dimensions k∈{1,2,3}, driven by a spatially homogeneous Gaussian noise that is white in time. They mainly consider the case where the spatial covariance is given by a Riesz kernel with exponent β. Using Malliavin calculus, they establish upper and lower bounds on the probabilities that the random field visits a deterministic subset of Rd, in terms, respectively, of Hausdorff measure and Newtonian capacity of this set. The dimension that appears in the Hausdorff measure is close to optimal, and shows that when d(2−β)>2(k+1), points are polar for u. Conversely, in low dimensions d, points are not polar. There is, however, an interval in which the question of polarity of points remains open.

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American Mathematical Soc.

Published Date

ISBN 10

1470414236

ISBN 13

9781470414238

A Minicourse on Stochastic Partial Differential Equations

By: Robert C. Dalang

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A Minicourse on Stochastic Partial Differential Equations

By: Robert C. Dalang

This title contains lectures that offer an introduction to modern topics in stochastic partial differential equations and bring together experts whose research is centered on the interface between Gaussian analysis, stochastic analysis, and stochastic PDEs.

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230

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540859934

ISBN 13

9783540859932

Sequential Stochastic Optimization

By: R. Cairoli,Robert C. Dalang

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Sequential Stochastic Optimization

By: R. Cairoli,Robert C. Dalang

Sequential Stochastic Optimization provides mathematicians andapplied researchers with a well-developed framework in whichstochastic optimization problems can be formulated and solved.Offering much material that is either new or has never beforeappeared in book form, it lucidly presents a unified theory ofoptimal stopping and optimal sequential control of stochasticprocesses. This book has been carefully organized so that littleprior knowledge of the subject is assumed; its only prerequisitesare a standard graduate course in probability theory and somefamiliarity with discrete-parameter martingales. Major topics covered in Sequential Stochastic Optimization include: * Fundamental notions, such as essential supremum, stopping points,accessibility, martingales and supermartingales indexed by INd * Conditions which ensure the integrability of certain suprema ofpartial sums of arrays of independent random variables * The general theory of optimal stopping for processes indexed byInd * Structural properties of information flows * Sequential sampling and the theory of optimal sequential control * Multi-armed bandits, Markov chains and optimal switching betweenrandom walks

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Page Count

348

Publisher

John Wiley & Sons

Published Date

ISBN 10

1118164407

ISBN 13

9781118164402

Topics in Spatial Stochastic Processes

Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, July 1-8, 2001

By: Vincenzo Capasso,Ely Merzbach,B. Gail Ivanoff,Marco Dozzi,Robert Dalang,Thomas Mountford

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Topics in Spatial Stochastic Processes

Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, July 1-8, 2001

By: Vincenzo Capasso,Ely Merzbach,B. Gail Ivanoff,Marco Dozzi,Robert Dalang,Thomas Mountford

The theory of stochastic processes indexed by a partially ordered set has been the subject of much research over the past twenty years. The objective of this CIME International Summer School was to bring to a large audience of young probabilists the general theory of spatial processes, including the theory of set-indexed martingales and to present the different branches of applications of this theory, including stochastic geometry, spatial statistics, empirical processes, spatial estimators and survival analysis. This theory has a broad variety of applications in environmental sciences, social sciences, structure of material and image analysis. In this volume, the reader will find different approaches which foster the development of tools to modelling the spatial aspects of stochastic problems.

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Page Count

256

Publisher

Springer

Published Date

ISBN 10

3540362592

ISBN 13

9783540362593

Book's by Robert C. Dalang

Seminar on Stochastic Analysis, Random Fields and Application [sic].

Seminar on Stochastic Analysis, Random Fields and Application [sic].

Hitting Probabilities for Nonlinear Systems of Stochastic Waves

Hitting Probabilities for Nonlinear Systems of Stochastic Waves

A Minicourse on Stochastic Partial Differential Equations

A Minicourse on Stochastic Partial Differential Equations

Sequential Stochastic Optimization

Sequential Stochastic Optimization

Topics in Spatial Stochastic Processes

Topics in Spatial Stochastic Processes

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