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2016, Springer series in operations research and financial engineering, ISBN 3319296787, xv, 320 pages
Book
2016, Springer Series in Operations Research and Financial Engineering, ISBN 3319296787
In this monograph the authors give a systematic approach to the probabilistic properties of the fixed point equation X=AX+B. A probabilistic study of the... 
Economic theory | Mathematics | Statistics | Probabilities
Web Resource
Stochastic Processes and their Applications, ISSN 0304-4149, 2019
For a time dependent family of probability measures (ρ ) we consider a kinetic-type evolution equation ∂ϕ ∕∂t+ϕ =Q̂ϕ where Q̂ is a smoothing transform and ϕ is... 
Kac model | Biggins martingale | Derivative martingale | Smoothing transform | Random trees | Kinetic equation
Journal Article
Journal of Applied Probability, ISSN 0021-9002, 12/2017, Volume 54, Issue 4, pp. 1089 - 1110
Given a sequence (M-k, Q(k))(k >= 1) of independent and identically distributed random vectors with nonnegative components, we consider the recursive Markov... 
Attractor set | transience | null recurrence | random difference equation | perpetuity | INVARIANT-MEASURES | Attraetor set | THEOREMS | RANDOM-WALK | CONVERGENCE | STATISTICS & PROBABILITY | Difference equations | Probability | Markov chains
Journal Article
Journal of Applied Probability, ISSN 0021-9002, 06/2018, Volume 55, Issue 2, pp. 368 - 389
An infinite convergent sum of independent and identically distributed random variables discounted by a multiplicative random walk is called perpetuity, because... 
Distribution tail | exponential moment | selfdecomposable distribution | perpetuity | REGULAR VARIATION | THIN TAILS | PRODUCTS | RENEWAL THEORY | STATISTICS & PROBABILITY | ASYMPTOTICS | Random walk | Random variables
Journal Article
ELECTRONIC JOURNAL OF PROBABILITY, ISSN 1083-6489, 2018, Volume 23
We study one-dimensional nearest neighbour random walk in site-dependent random environment. We establish precise (sharp) large deviations in the so-called... 
large deviations | branching process with immigration | TIMES | DIMENSIONAL RANDOM-WALK | EQUATIONS | STATISTICS & PROBABILITY | random walk in random environment
Journal Article
Journal of Difference Equations and Applications, ISSN 1023-6198, 02/2014, Volume 20, Issue 2, pp. 188 - 209
We consider solutions of the stochastic equation , where N is a random natural number, B and A i are random positive numbers and X i are independent copies of... 
linear stochastic equation | large deviations | primary 60H25 | secondary 60J80, 60F10 | smoothing transform | regular variation | MATHEMATICS, APPLIED | 60F10 | RENEWAL THEORY | secondary 60J80 | X-N | CONVERGENCE | MINIMAL POSITION | FIXED-POINTS | Tangents | Reproduction | Difference equations | Asymptotic properties | Mathematical analysis | Images | Stochasticity
Journal Article
Journal of Difference Equations and Applications, ISSN 1023-6198, 11/2014, Volume 20, Issue 11, pp. 1523 - 1567
Let Z be a random variable with values in a proper closed convex cone , A a random endomorphism of C and N a random integer. We assume that Z, A, N are... 
products of random matrices | renewal theorem | asymptotic behaviour | fixed points | Mandelbrot's cascade | MATHEMATICS, APPLIED | LAW | RANDOM DIFFERENCE-EQUATIONS | RENEWAL THEORY | RANDOM MATRICES | PRODUCTS | THEOREMS | SMOOTHING TRANSFORM | FIXED-POINTS | BRANCHING RANDOM-WALK | Reproduction | Law | Maps | Mathematical analysis | Images | Eigenvalues | Transformations | Random variables
Journal Article
Stochastic Processes and their Applications, ISSN 0304-4149, 06/2013, Volume 123, Issue 6, pp. 1947 - 1986
Let be a fixed integer and a random element of . We consider solutions of multivariate smoothing transforms, i.e. random variables satisfying where denotes... 
Branching | Renewal theory | General theory | Distributions | TREES | MARKOV-CHAINS | LIMIT-THEOREM | STATISTICS & PROBABILITY | VARIANCE | RECURSIVE ALGORITHMS | FIXED-POINTS | Mathematics - Probability
Journal Article
Probability Theory and Related Fields, ISSN 0178-8051, 2009, Volume 145, Issue 4, pp. 385 - 420
We consider a stochastic recursion Xn+1 = Mn+1Xn + Q(n+1), (n is an element of N), where (Q(n), M-n) are i.i.d. random variables such that Qn are translations,... 
60J10 | 60K05 | STATISTICS & PROBABILITY | PRODUCTS | MATRICES | BEHAVIOR | Analysis | Universities and colleges | Probability | Mathematics
Journal Article
Communications in Partial Differential Equations, ISSN 0360-5302, 10/2006, Volume 31, Issue 10, pp. 1547 - 1589
On a Lie group S = NA, that is a split extension of a nilpotent Lie group N by a one-parameter group of automorphisms A, a probability measure μ is considered... 
22E25 | 31B25 | Invariant measure | 60J60 | Subelliptic operator | 22E30 | Heat semigroup | Nilpotent Lie group | 43A80 | MATHEMATICS | DEGENERATE ELLIPTIC-OPERATORS | MATHEMATICS, APPLIED | heat semigroup | nilpotent Lie group | NEGATIVE CURVATURE | PRODUCTS | invariant measure | MANIFOLDS | subelliptic operator
Journal Article
Annales de l'Institut Henri Poincare / Probabilites et statistiques, ISSN 0246-0203, 2007, Volume 43, Issue 4, pp. 417 - 440
Let be a subgroup of and let ( ) be a sequence of i.i.d. random variables with values in and law . Under some natural conditions there exists a unique... 
Stationary measure | Solvable Lie groups | Poisson kernel | HOMOGENEOUS MANIFOLDS | stationary measure | solvable Lie groups | NEGATIVE CURVATURE | PRODUCTS | STATISTICS & PROBABILITY | OPERATORS
Journal Article
Journal d’Analyse Mathématique, ISSN 0021-7670, 12/2006, Volume 98, Issue 1, pp. 113 - 143
We define and investigate the Riesz transform associated with the differential operatorL λ f(θ)=−f"(θ)−2λ cot’θ. We prove that it can be defined as a principal... 
Abstract Harmonic Analysis | Mathematics | Functional Analysis | Dynamical Systems and Ergodic Theory | Analysis | Partial Differential Equations | MATHEMATICS | ORNSTEIN-UHLENBECK SEMIGROUP | OSCILLATION | EXPANSIONS | Polynomials
Journal Article
07/2016, 1st ed. 2016, Springer series in operations research and financial engineering, ISBN 3319296787, 325
In this monograph the authors give a systematic approach to the probabilistic properties of the fixed point equation X=AX+B. A probabilistic study of the... 
Economics | Stochastic processes | Economic theory | Probability Theory and Stochastic Processes | Mathematics | Statistics for Business/Economics/Mathematical Finance/Insurance | Economic Theory/Quantitative Economics/Mathematical Methods | Stochastic models
eBook
The Journal of Geometric Analysis, ISSN 1050-6926, 9/2004, Volume 14, Issue 3, pp. 457 - 486
Journal Article
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