1. Introduction ................................................. 5
2. Preliminaries ................................................ 7
2.1. Basic notions ........................................... 7
2.2. Dimensions of measures .................................. 8
3. Properties of Markov operators ............................... 9
3.1. Markov operators ........................................ 9
3.2. Criteria for asymptotic stability ...................... 11
4. Random dynamical systems with jumps ......................... 13
4.1. Introduction ........................................... 13
4.2. Discrete-time random dynamical systems ................. 15
4.3. Continuous-time random dynamical systems ............... 25
5. Dimensions of invariant measures of random dynamical
systems with jumps .......................................... 41
5.1. The lower pointwise dimension of an invariant
measure ................................................ 41
5.2. The upper bound for the concentration dimension of
an invariant measure ................................... 45
5.3. Relationship between discrete and continuous-time
random dynamical systems ............................... 46
6. Applications ................................................ 51
6.1. Iterated function systems .............................. 52
6.2. Irreducible Markov systems ............................. 53
6.3. Mathematical theory of the cell cycle .................. 59
6.4. Randomly connected differential equations with
Poisson-type perturbations ............................. 60
References ..................................................... 64
Index .......................................................... 67
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